A template is a prototype for a sequence of DAEs which can be used repeatedly in different instantiations. Normally, but not always, the template corresponds to some subsystem of a physical-model description of a system, like a tank or distillation tray. The key characteristics of a template are: the number of integration states it incorporates (typically fixed), the number of nonstate variables it incorporates (typically fixed), its input and output connections to other templates, and external sources (forcing functions) and sinks. State variables participate in the overall DASSL integration process. Nonstates are defined as variables which, given the states of a template alone, may be computed uniquely. They are essentially local tear variables. It is up to the template designer whether or not to use such local tear variables: They impact the numerical quality of the solution, in principle. Alternative formulations, where all variables of a template are treated as states, can be posed and comparisons made. Because of the superlinear growth of linear algebra complexity, the introduction of extra integration states must be justified on the basis of numerical accuracy. Otherwise, they artificially slow down the problem solution, perhaps significantly. Nonstates are extremely convenient and practically useful; they appear in all the dynamic simulators we have come across.
The template state and nonstate structure imply a two-phase residual
computation. First, given a state 
, the non-states of each template
are updated on a template-by-template basis. Then, given its states and
non-states, inputs from other templates and external inputs, each template's
residuals may be computed. In the sequential implementation, this poses no
particular nuisances, other than having two evaluation loops over all templates.
However, in concurrent evaluation, a communication phase intervenes between
nonstate and residual updates. This communication phase transmits
all states and nonstates appearing as outputs of templates to their
corresponding inputs at other templates. This transmission mechanism is
considered below under concurrent formulation.